FIA NLS Models: Biomass Growth vs. Stand Age
JAH
2022-12-14
Background
This document has nls (non-linear least squares) regression fits using the log-normal functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. stand age relationships. This functional form is commonly used in growth analyses, and permits a flexible shape to fit to data with an intermediate maximum (i.e., “hump” shaped) curve. As in our models of biomass growth vs. biomass, we use themass balance biomass growth method for the plot biomass growth (\(G\)) calculation (briefly, plot biomass growth is a function of the change in plot biomass plus any losses due to mortality or harvest over time: \(G_{MB} = (\Delta B + M_t + C_t) / REMPER\), where \(\Delta B\) is change in plot biomass over a census interval ( \(\Delta B = B_{t + \Delta g} - B_t\) ), and \(M_t\) and \(C_t\) is the biomass of trees that died or were harvested, respectively, between two plot measurements. note: \(REMPER\) is time between two plot measurement invetvals (FIA re-measurment period). For additional details see supplementary methods. Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following non-linear model is considered: \(G = (1 + (yr-1990) \cdot ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(StdAge_{t1}\) is the FIA-estimated stand age at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(G\), \(c\): the \(StdAge_{t1}\) value at peak \(G\), and \(d\): the curve shape parameter.
Data have increasing variance in \(G\) with increasing \(StdAge_{t1}\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {StdAge_{t1}^2}\) in equal-sample sized plot biomass bins (n=20 where applicable, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.
Model selection is done to determine the best fitting models, considering the inclusion of \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. Thus, the following three models are considered:
model 1: simple model \(G = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 2: phi model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left( StdAge_{t1} /c \right)} {d} \right]} ^2 \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROG_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1760 observations.
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6869 2901.4
## 2 6868 2897.9 1 3.58 8.4899 0.003583 **
## 3 6816 2053.4 52 844.44 53.9035 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 29461.42
## 2 2 29454.93
## 3 3 26942.43##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.175722 0.179713 0.978 0.3282
## phi 0.012249 0.005014 2.443 0.0146 *
## alpha 0.647140 0.033805 19.143 <2e-16 ***
## a 0.000000 2.567372 0.000 1.0000
## b 3.468659 2.556471 1.357 0.1749
## c 31.531484 2.197624 14.348 <2e-16 ***
## d 2.807170 1.242763 2.259 0.0239 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5489 on 6816 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (54 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 19351 8864.8
## 2 19346 8847.1 5 17.6 7.714 2.946e-07 ***
## 3 18857 4837.7 489 4009.5 31.961 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 83315.42
## 2 2 83265.16
## 3 3 70430.13##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.371292 0.183338 7.480 7.78e-14 ***
## phi 0.022177 0.003247 6.830 8.78e-12 ***
## alpha 0.760152 0.021729 34.984 < 2e-16 ***
## a 0.910942 0.149971 6.074 1.27e-09 ***
## b 1.473072 0.146625 10.047 < 2e-16 ***
## c 21.870646 0.551908 39.627 < 2e-16 ***
## d 1.974895 0.160872 12.276 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5065 on 18857 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3851 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 45 rows containing missing values (geom_point).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7319 3437.6
## 2 7318 3428.8 1 8.85 18.899 1.397e-05 ***
## 3 7254 2939.9 64 488.85 18.846 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 34070.15
## 2 2 34053.26
## 3 3 32723.77##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.731059 0.141839 -5.154 2.62e-07 ***
## phi 0.019550 0.005574 3.507 0.000456 ***
## alpha 0.762600 0.040154 18.992 < 2e-16 ***
## a 2.765891 0.736279 3.757 0.000174 ***
## b 1.866948 0.732518 2.549 0.010834 *
## c 37.622145 3.355077 11.213 < 2e-16 ***
## d 1.800177 0.531966 3.384 0.000718 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6366 on 7254 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (72 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 6 rows containing missing values (geom_point).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5044 2430.6
## 2 5043 2429.2 1 1.43 2.9759 0.08458 .
## 3 4823 1030.9 220 1398.27 29.7341 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25434.95
## 2 2 25433.97
## 3 3 20509.56##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.009831 0.259463 -0.038 0.9698
## phi 0.021208 0.009599 2.209 0.0272 *
## alpha 0.754175 0.046147 16.343 < 2e-16 ***
## a 1.873987 0.302299 6.199 6.15e-10 ***
## b 1.512030 0.292885 5.163 2.53e-07 ***
## c 48.261189 3.829558 12.602 < 2e-16 ***
## d 1.759624 0.320971 5.482 4.41e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4623 on 4823 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1015 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 7 rows containing missing values (geom_point).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Error in nls(fg2_2, data = G_223, start = c(ge = ge.start, a = a.start, :
## parameters without starting value in 'data': phi
## model AIC
## 1 1 41571.02
## 2 2 NA
## 3 3 37051.42##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.430060 0.154490 -2.784 0.00539 **
## phi 0.000000 0.006842 0.000 1.00000
## alpha 0.610247 0.043518 14.023 < 2e-16 ***
## a 1.932355 0.632130 3.057 0.00224 **
## b 1.921786 0.623188 3.084 0.00205 **
## c 27.166651 1.999717 13.585 < 2e-16 ***
## d 1.710858 0.425897 4.017 5.94e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5408 on 8729 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1274 observations deleted due to missingness)summary
- simple model: fits
- phi model: does not fit
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 6 rows containing missing values (geom_point).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13446 7694.3
## 2 13445 7690.4 1 3.88 6.7776 0.009241 **
## 3 13194 6475.2 251 1215.26 9.8655 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70330.21
## 2 2 70325.44
## 3 3 67126.40##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.087217 0.169513 6.414 1.47e-10 ***
## phi 0.007909 0.004533 1.745 0.081 .
## alpha 0.882295 0.020065 43.973 < 2e-16 ***
## a 2.279044 0.222624 10.237 < 2e-16 ***
## b 3.025758 0.212841 14.216 < 2e-16 ***
## c 17.670790 0.409384 43.164 < 2e-16 ***
## d 1.471406 0.101786 14.456 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7005 on 13194 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (316 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 30 rows containing missing values (geom_point).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13504 9637.4
## 2 13503 9627.8 1 9.63 13.5009 0.0002394 ***
## 3 13220 8281.9 283 1345.94 7.5918 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 70511.84
## 2 2 70500.33
## 3 3 67414.37##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.090965 0.193247 5.645 1.68e-08 ***
## phi 0.012699 0.004842 2.623 0.00873 **
## alpha 0.878838 0.019490 45.091 < 2e-16 ***
## a 3.024828 0.116153 26.042 < 2e-16 ***
## b 2.215523 0.109583 20.218 < 2e-16 ***
## c 15.764213 0.430152 36.648 < 2e-16 ***
## d 0.898401 0.050710 17.716 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7915 on 13220 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (402 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 66 rows containing missing values (geom_point).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Error in nls(fg2_1, data = G_234, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(fg2_2, data = G_234, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 6972.096##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.49422 1.17974 1.267 0.205534
## phi 0.00000 0.02294 0.000 1.000000
## alpha 0.81742 0.08559 9.550 < 2e-16 ***
## a 3.25252 0.62763 5.182 2.54e-07 ***
## b 1.60883 0.52220 3.081 0.002107 **
## c 17.83216 2.52293 7.068 2.54e-12 ***
## d 0.68248 0.20369 3.351 0.000829 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8154 on 1315 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (66 observations deleted due to missingness)summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: fits ## plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90233, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.3394, p-value = 9.324e-08
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 5 rows containing missing values (geom_point).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1888 981.71
## 2 1887 981.71 1 0.00 0.000 1
## 3 1772 366.23 115 615.48 25.895 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9553.901
## 2 2 9555.901
## 3 3 7360.235##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.42081 0.50776 0.829 0.407354
## phi 0.01688 0.01280 1.319 0.187293
## alpha 0.39359 0.10471 3.759 0.000176 ***
## a 0.00000 7.48138 0.000 1.000000
## b 2.75477 7.47785 0.368 0.712626
## c 29.12100 7.86923 3.701 0.000222 ***
## d 3.98974 6.44419 0.619 0.535915
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4546 on 1772 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (516 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.82033, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.3049, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 2 rows containing missing values (geom_point).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 710 1009.74
## 2 709 993.90 1 15.841 11.3005 0.0008165 ***
## 3 666 874.66 43 119.237 2.1114 6.801e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3560.631
## 2 2 3551.325
## 3 3 3316.266##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.47159 1.57754 0.933 0.351240
## phi 0.07749 0.03138 2.470 0.013771 *
## alpha 0.57688 0.18640 3.095 0.002052 **
## a 0.79526 0.55225 1.440 0.150329
## b 2.20051 0.75723 2.906 0.003782 **
## c 15.62073 1.93811 8.060 3.54e-15 ***
## d 1.28673 0.37411 3.439 0.000619 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.146 on 666 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (44 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92581, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.18, p-value = 2.915e-05
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 2 rows containing missing values (geom_point).
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
411 - Everglades
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6765 1889.9
## 2 6764 1879.6 1 10.281 36.998 1.247e-09 ***
## 3 6740 1749.8 24 129.814 20.835 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 25839.54
## 2 2 25804.61
## 3 3 25259.82##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.850679 0.215547 3.947 8.01e-05 ***
## phi 0.023449 0.004584 5.116 3.21e-07 ***
## alpha 0.627001 0.029034 21.595 < 2e-16 ***
## a 2.395907 0.162710 14.725 < 2e-16 ***
## b 0.669053 0.118100 5.665 1.53e-08 ***
## c 29.566789 2.152052 13.739 < 2e-16 ***
## d 1.014318 0.225290 4.502 6.84e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5095 on 6740 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (25 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8308 4863.8
## 2 8307 4863.8 1 0.00 0.000 0.9998
## 3 8252 4464.8 55 398.96 13.407 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 40946.90
## 2 2 40948.90
## 3 3 40032.35##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.379874 0.205871 1.845 0.065 .
## phi 0.000000 0.006671 0.000 1.000
## alpha 0.831928 0.056198 14.803 < 2e-16 ***
## a 2.837387 0.308199 9.206 < 2e-16 ***
## b 1.567034 0.260530 6.015 1.88e-09 ***
## c 26.790439 2.070126 12.941 < 2e-16 ***
## d 1.190169 0.241636 4.925 8.58e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7356 on 8252 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (56 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
predict and plot
## Warning: Removed 2 rows containing missing values (geom_point).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 890 537.81
## 2 889 537.81 1 0.000 0.0000 1
## 3 882 515.61 7 22.204 5.4262 4.128e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3747.851
## 2 2 3749.851
## 3 3 3696.417##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.88192 2.09581 1.852 0.064327 .
## phi 0.00000 0.02552 0.000 1.000000
## alpha 0.89195 0.14974 5.957 3.72e-09 ***
## a 1.39795 0.34310 4.074 5.03e-05 ***
## b 0.87413 0.32246 2.711 0.006842 **
## c 32.18412 2.98916 10.767 < 2e-16 ***
## d 0.39970 0.11321 3.530 0.000436 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7646 on 882 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (7 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9565, p-value = 1.42e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.926, p-value = 0.05411
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1000 560.60
## 2 999 552.70 1 7.902 14.2827 0.0001666 ***
## 3 986 491.02 13 61.681 9.5278 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4301.062
## 2 2 4288.796
## 3 3 4128.190##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.83325 1.71080 1.656 0.09802 .
## phi 0.06188 0.02469 2.506 0.01235 *
## alpha 0.83322 0.10345 8.055 2.29e-15 ***
## a 1.56723 0.38924 4.026 6.10e-05 ***
## b 1.02877 0.36360 2.829 0.00476 **
## c 8.22702 4.42140 1.861 0.06308 .
## d 1.36317 0.64509 2.113 0.03484 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7057 on 986 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (13 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96553, p-value = 1.401e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.6924, p-value = 2.196e-11
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3140 2646.7
## 2 3139 2646.6 1 0.127 0.1508 0.6978
## 3 3126 2505.4 13 141.214 13.5534 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 17325.39
## 2 2 17327.24
## 3 3 17111.31##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.68631 0.28189 -5.982 2.45e-09 ***
## phi 0.03281 0.01781 1.842 0.0656 .
## alpha 1.00975 0.07255 13.918 < 2e-16 ***
## a 6.71584 0.63106 10.642 < 2e-16 ***
## b 5.11669 0.94827 5.396 7.33e-08 ***
## c 33.89591 1.57146 21.570 < 2e-16 ***
## d 0.34932 0.05348 6.531 7.58e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8952 on 3126 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (91 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92849, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -13.637, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 14 rows containing missing values (geom_point).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1681 601.84
## 2 1680 564.32 1 37.518 111.6926 < 2.2e-16 ***
## 3 1667 553.48 13 10.846 2.5128 0.002055 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8778.075
## 2 2 8671.552
## 3 3 8594.167##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.11595 0.28437 -7.441 1.59e-13 ***
## phi 0.22245 0.01615 13.775 < 2e-16 ***
## alpha 0.63860 0.11361 5.621 2.22e-08 ***
## a 0.00000 15.61528 0.000 1.000
## b 9.69748 15.55236 0.624 0.533
## c 41.76697 9.84387 4.243 2.33e-05 ***
## d 3.08338 3.19925 0.964 0.335
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5762 on 1667 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (303 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89623, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.89111, p-value = 0.3729
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 9 rows containing missing values (geom_point).
plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 360 174.32
## 2 359 171.92 1 2.4066 5.0256 0.025586 *
## 3 358 167.42 1 4.4942 9.6100 0.002088 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 1014.707
## 2 2 1011.633
## 3 3 1003.964##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.35177 0.35314 -6.660 1.04e-10 ***
## phi 0.04249 0.03040 1.398 0.163042
## alpha 0.53619 0.15685 3.418 0.000702 ***
## a 0.00000 5.08614 0.000 1.000000
## b 3.54153 5.16095 0.686 0.493020
## c 60.11727 17.06244 3.523 0.000481 ***
## d 2.03511 2.15536 0.944 0.345698
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6839 on 358 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94875, p-value = 6.111e-10
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.2763, p-value = 0.2018
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1736 1579.8
## 2 1735 1566.4 1 13.436 14.882 0.0001186 ***
## 3 1718 1408.5 17 157.914 11.330 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 5243.073
## 2 2 5230.203
## 3 3 5027.467##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.43950 0.72527 -0.606 0.544611
## phi 0.07592 0.01579 4.808 1.66e-06 ***
## alpha 0.60685 0.06216 9.762 < 2e-16 ***
## a 0.50536 0.45171 1.119 0.263388
## b 1.39227 0.48322 2.881 0.004010 **
## c 52.27252 4.00432 13.054 < 2e-16 ***
## d 1.68705 0.44665 3.777 0.000164 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9055 on 1718 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (31 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.85663, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.9566, p-value = 7.173e-07
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 7 rows containing missing values (geom_point).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2527 1847.2
## 2 2526 1843.7 1 3.498 4.7926 0.02867 *
## 3 2484 1677.5 42 166.126 5.8569 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 9333.635
## 2 2 9330.836
## 3 3 9043.459##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.70989 0.51904 -1.368 0.171534
## phi 0.02565 0.01852 1.385 0.166144
## alpha 0.82947 0.05540 14.972 < 2e-16 ***
## a 0.77371 0.65074 1.189 0.234570
## b 1.89238 0.68717 2.754 0.005932 **
## c 61.36711 5.77057 10.635 < 2e-16 ***
## d 2.10362 0.57479 3.660 0.000258 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8218 on 2484 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (121 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88452, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.8136, p-value = 9.522e-12
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 28 rows containing missing values (geom_point).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1699 872.98
## 2 1698 871.99 1 0.987 1.9228 0.1657
## 3 1669 777.32 29 94.663 7.0087 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6978.661
## 2 2 6978.732
## 3 3 6737.088##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.07404 0.85812 0.086 0.931
## phi 0.00470 0.02034 0.231 0.817
## alpha 0.85634 0.05823 14.706 < 2e-16 ***
## a 1.43729 0.29460 4.879 1.17e-06 ***
## b 2.34177 0.46362 5.051 4.88e-07 ***
## c 49.87354 2.07374 24.050 < 2e-16 ***
## d 1.09119 0.09957 10.959 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6825 on 1669 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (77 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93034, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.5801, p-value = 2.403e-08
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 14 rows containing missing values (geom_point).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Error in nls(fg2_1, data = G_M334, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(fg2_2, data = G_M334, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 1377.238##
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 +
## phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -3.74019 0.09721 -38.477 < 2e-16 ***
## phi 0.09723 0.02834 3.431 0.000674 ***
## alpha 0.75357 0.18506 4.072 5.77e-05 ***
## a 0.00000 1728.64931 0.000 1.000000
## b 5.19647 1728.30661 0.003 0.997603
## c 67.00547 108.86401 0.615 0.538629
## d 4.59576 789.29208 0.006 0.995358
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4652 on 348 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (104 observations deleted due to missingness)summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91388, p-value = 2.264e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.4979, p-value = 0.01249
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_point).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3 |
| 212 | Laurentian Mixed Forest | 3 |
| 221 | Eastern Broadleaf Forest | 3 |
| 222 | Midwest Broadleaf Forest | 3 |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3 |
| 232 | Outer Coastal Plain Mixed Forest | 3 |
| 234 | Lower Mississippi Riverine Forest | 3 |
| 242 | Pacific Lowland Mixed Forest | NA |
| 251 | Prairie Parkland (Temperate) | 3 |
| 255 | Prairie Parkland (Subtropical) | 3 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | NA |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | NA |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3 |
| M242 | Cascade Mixed Forest | 3 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 3 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 3 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3 |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.variance | ge.2.5 | ge.97.5 | phi | phi.variance | phi.2.5 | phi.97.5 | alpha | alpha.variance | alpha.2.5 | alpha.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6877 | 2876 | 0.1757217 | 0.0322968 | -0.1765723 | 0.5280157 | 0.0122492 | 0.0000251 | 0.0024208 | 0.0220776 | 0.6471401 | 0.0011428 | 0.5808719 | 0.7134083 | 0.0000000 | -5.0328500 | 5.032850 | 3.4686588 | -1.5428214 | 8.4801390 | 31.531484 | 27.2234549 | 35.83951 | 2.8071701 | 0.3709672 | 5.2433731 |
| 212 | Laurentian Mixed Forest | east | 22715 | 9499 | 1.3712921 | 0.0336129 | 1.0119325 | 1.7306517 | 0.0221771 | 0.0000105 | 0.0158122 | 0.0285419 | 0.7601525 | 0.0004721 | 0.7175621 | 0.8027429 | 0.9109417 | 0.6169850 | 1.204898 | 1.4730721 | 1.1856744 | 1.7604698 | 21.870646 | 20.7888568 | 22.95243 | 1.9748949 | 1.6595713 | 2.2902184 |
| 221 | Eastern Broadleaf Forest | east | 7333 | 3571 | -0.7310590 | 0.0201183 | -1.0091047 | -0.4530133 | 0.0195496 | 0.0000311 | 0.0086221 | 0.0304770 | 0.7625996 | 0.0016124 | 0.6838854 | 0.8413138 | 2.7658911 | 1.3225695 | 4.209213 | 1.8669476 | 0.4309986 | 3.3028965 | 37.622145 | 31.0452181 | 44.19907 | 1.8001769 | 0.7573684 | 2.8429855 |
| 222 | Midwest Broadleaf Forest | east | 5845 | 2589 | -0.0098311 | 0.0673213 | -0.5184979 | 0.4988356 | 0.0212082 | 0.0000921 | 0.0023900 | 0.0400265 | 0.7541747 | 0.0021295 | 0.6637062 | 0.8446432 | 1.8739873 | 1.2813427 | 2.466632 | 1.5120302 | 0.9378419 | 2.0862185 | 48.261189 | 40.7535103 | 55.76887 | 1.7596238 | 1.1303752 | 2.3888723 |
| 223 | Central Interior Broadleaf Forest | east | 10010 | 3864 | -0.4300605 | 0.0238672 | -0.7328976 | -0.1272234 | 0.0000000 | 0.0000468 | -0.0134128 | 0.0134128 | 0.6102470 | 0.0018938 | 0.5249408 | 0.6955533 | 1.9323553 | 0.6932307 | 3.171480 | 1.9217860 | 0.7001901 | 3.1433819 | 27.166651 | 23.2467347 | 31.08657 | 1.7108584 | 0.8760004 | 2.5457164 |
| 231 | Southeastern Mixed Forest | east | 13517 | 6193 | 1.0872168 | 0.0287345 | 0.7549477 | 1.4194859 | 0.0079088 | 0.0000205 | -0.0009756 | 0.0167932 | 0.8822954 | 0.0004026 | 0.8429659 | 0.9216249 | 2.2790445 | 1.8426686 | 2.715420 | 3.0257576 | 2.6085578 | 3.4429573 | 17.670790 | 16.8683377 | 18.47324 | 1.4714062 | 1.2718904 | 1.6709221 |
| 232 | Outer Coastal Plain Mixed Forest | east | 13629 | 6626 | 1.0909652 | 0.0373445 | 0.7121729 | 1.4697576 | 0.0126993 | 0.0000234 | 0.0032082 | 0.0221903 | 0.8788383 | 0.0003799 | 0.8406343 | 0.9170423 | 3.0248278 | 2.7971517 | 3.252504 | 2.2155226 | 2.0007250 | 2.4303203 | 15.764214 | 14.9210544 | 16.60737 | 0.8984005 | 0.7990007 | 0.9978004 |
| 234 | Lower Mississippi Riverine Forest | east | 1388 | 778 | 1.4942188 | 1.3917795 | -0.8201536 | 3.8085911 | 0.0000000 | 0.0005261 | -0.0449981 | 0.0449981 | 0.8174169 | 0.0073257 | 0.6495081 | 0.9853257 | 3.2525184 | 2.0212509 | 4.483786 | 1.6088252 | 0.5843812 | 2.6332693 | 17.832162 | 12.8827518 | 22.78157 | 0.6824795 | 0.2828883 | 1.0820707 |
| 242 | Pacific Lowland Mixed Forest | pacific | 83 | 83 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 251 | Prairie Parkland (Temperate) | east | 2295 | 906 | 0.4208094 | 0.2578200 | -0.5750617 | 1.4166806 | 0.0168846 | 0.0001638 | -0.0082195 | 0.0419888 | 0.3935897 | 0.0109646 | 0.1882173 | 0.5989622 | 0.0000000 | -14.6732552 | 14.673255 | 2.7547694 | -11.9115628 | 17.4211017 | 29.121003 | 13.6870608 | 44.55495 | 3.9897412 | -8.6492645 | 16.6287469 |
| 255 | Prairie Parkland (Subtropical) | east | 717 | 319 | 1.4715937 | 2.4886282 | -1.6259544 | 4.5691419 | 0.0774910 | 0.0009845 | 0.0158825 | 0.1390995 | 0.5768757 | 0.0347441 | 0.2108777 | 0.9428737 | 0.7952626 | -0.2891058 | 1.879631 | 2.2005057 | 0.7136645 | 3.6873469 | 15.620730 | 11.8151965 | 19.42626 | 1.2867271 | 0.5521553 | 2.0212988 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 25 | 25 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 163 | 161 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 218 | 218 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 331 | 255 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 232 | 128 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 341 | Intermountain Semi-Desert and Desert | interior west | 66 | 64 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 124 | 123 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 411 | Everglades | east | 96 | 63 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6772 | 3006 | 0.8506786 | 0.0464607 | 0.4281377 | 1.2732195 | 0.0234487 | 0.0000210 | 0.0144631 | 0.0324344 | 0.6270009 | 0.0008430 | 0.5700847 | 0.6839171 | 2.3959066 | 2.0769427 | 2.714870 | 0.6690529 | 0.4375387 | 0.9005672 | 29.566789 | 25.3480873 | 33.78549 | 1.0143181 | 0.5726788 | 1.4559574 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8315 | 3810 | 0.3798736 | 0.0423827 | -0.0236846 | 0.7834318 | 0.0000000 | 0.0000445 | -0.0130773 | 0.0130773 | 0.8319284 | 0.0031582 | 0.7217658 | 0.9420911 | 2.8373869 | 2.2332400 | 3.441534 | 1.5670341 | 1.0563296 | 2.0777385 | 26.790439 | 22.7324710 | 30.84841 | 1.1901695 | 0.7165016 | 1.6638373 |
| M223 | Ozark Broadleaf Forest Meadow | east | 896 | 349 | 3.8819194 | 4.3924187 | -0.2314369 | 7.9952758 | 0.0000000 | 0.0006513 | -0.0500874 | 0.0500874 | 0.8919472 | 0.0224223 | 0.5980573 | 1.1858370 | 1.3979515 | 0.7245642 | 2.071339 | 0.8741318 | 0.2412521 | 1.5070115 | 32.184124 | 26.3174182 | 38.05083 | 0.3996992 | 0.1774979 | 0.6219005 |
| M231 | Ouachita Mixed Forest | east | 1006 | 495 | 2.8332512 | 2.9268445 | -0.5239808 | 6.1904831 | 0.0618791 | 0.0006095 | 0.0134331 | 0.1103252 | 0.8332165 | 0.0107009 | 0.6302183 | 1.0362147 | 1.5672319 | 0.8033972 | 2.331067 | 1.0287701 | 0.3152511 | 1.7422890 | 8.227022 | -0.4494142 | 16.90346 | 1.3631726 | 0.0972655 | 2.6290796 |
| M242 | Cascade Mixed Forest | pacific | 3224 | 3207 | -1.6863076 | 0.0794597 | -2.2390078 | -1.1336075 | 0.0328095 | 0.0003173 | -0.0021192 | 0.0677381 | 1.0097463 | 0.0052638 | 0.8674925 | 1.1520002 | 6.7158353 | 5.4784970 | 7.953174 | 5.1166890 | 3.2573890 | 6.9759891 | 33.895910 | 30.8147167 | 36.97710 | 0.3493224 | 0.2444564 | 0.4541883 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1977 | 1807 | -2.1159462 | 0.0808660 | -2.6737052 | -1.5581872 | 0.2224490 | 0.0002608 | 0.1907744 | 0.2541236 | 0.6386041 | 0.0129071 | 0.4157720 | 0.8614363 | 0.0000000 | -30.6276147 | 30.627615 | 9.6974846 | -20.8067314 | 40.2017006 | 41.766965 | 22.4593149 | 61.07462 | 3.0833786 | -3.1915868 | 9.3583439 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 30 | 26 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 367 | 367 | -2.3517700 | 0.1247053 | -3.0462524 | -1.6572876 | 0.0424936 | 0.0009242 | -0.0172926 | 0.1022799 | 0.5361936 | 0.0246028 | 0.2277251 | 0.8446621 | 0.0000000 | -10.0024735 | 10.002474 | 3.5415332 | -6.6080480 | 13.6911145 | 60.117269 | 26.5620659 | 93.67247 | 2.0351118 | -2.2036387 | 6.2738624 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1756 | 1756 | -0.4394975 | 0.5260216 | -1.8620095 | 0.9830145 | 0.0759209 | 0.0002494 | 0.0449473 | 0.1068945 | 0.6068543 | 0.0038642 | 0.4849311 | 0.7287774 | 0.5053632 | -0.3805895 | 1.391316 | 1.3922719 | 0.4445098 | 2.3400341 | 52.272520 | 44.4186644 | 60.12638 | 1.6870535 | 0.8110138 | 2.5630932 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2612 | 2602 | -0.7098862 | 0.2694041 | -1.7276847 | 0.3079123 | 0.0256535 | 0.0003430 | -0.0106646 | 0.0619715 | 0.8294692 | 0.0030694 | 0.7208304 | 0.9381079 | 0.7737062 | -0.5023491 | 2.049762 | 1.8923794 | 0.5448956 | 3.2398632 | 61.367106 | 50.0514907 | 72.68272 | 2.1036231 | 0.9765099 | 3.2307362 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1753 | 1742 | 0.0740389 | 0.7363628 | -1.6090579 | 1.7571357 | 0.0047003 | 0.0004137 | -0.0351939 | 0.0445945 | 0.8563386 | 0.0033909 | 0.7421249 | 0.9705523 | 1.4372869 | 0.8594631 | 2.015111 | 2.3417687 | 1.4324324 | 3.2511050 | 49.873539 | 45.8061307 | 53.94095 | 1.0911851 | 0.8958840 | 1.2864863 |
| M334 | Black Hills Coniferous Forest | interior west | 459 | 181 | -3.7401899 | 0.0094489 | -3.9313741 | -3.5490057 | 0.0972250 | 0.0008030 | 0.0414904 | 0.1529597 | 0.7535661 | 0.0342465 | 0.3895930 | 1.1175392 | 0.0000000 | -3399.9147613 | 3399.914761 | 5.1964723 | -3394.0442740 | 3404.4372185 | 67.005467 | -147.1087216 | 281.11966 | 4.5957627 | -1547.7872271 | 1556.9787525 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 220 | 220 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot phi (effect of DeltaPDSI)
plot alpha (biomass growth compensation effect)
plot a coefficient
## Warning: Removed 15 rows containing missing values (geom_point).
plot b coefficient
## Warning: Removed 15 rows containing missing values (geom_point).
plot c coefficient
## Warning: Removed 1 rows containing missing values (geom_hline).## Warning: Removed 16 rows containing missing values (geom_point).
plot d coefficient
## Warning: Removed 15 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass growth enhancement factor in % 2000-2021)
## region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1 entire US 0.32298228 0.07217642 0.4644481 0.1815165
## 2 pacific -0.15936993 0.01795158 -0.1241848 -0.1945550
## 3 east 0.55192458 0.05647196 0.6626096 0.4412395
## 4 interior west -0.06957237 0.04120795 0.0111952 -0.1503399phi (effect of DeltaPDSI)
## region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1 entire US 0.024056979 0.002108731 0.028190093
## 2 pacific 0.008755896 0.001107489 0.010926574
## 3 east 0.011132791 0.001371046 0.013820041
## 4 interior west 0.004168293 0.001157778 0.006437538
## 95 % CI, lower
## 1 0.019923866
## 2 0.006585218
## 3 0.008445541
## 4 0.001899048alpha (biomass growth compensation effect)
## region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1 entire US 0.75612701 0.010455205 0.77661921
## 2 pacific 0.07582588 0.005356807 0.08632522
## 3 east 0.59313953 0.008153682 0.60912075
## 4 interior west 0.08716159 0.003759442 0.09453010
## 95 % CI, lower
## 1 0.73563480
## 2 0.06532654
## 3 0.57715832
## 4 0.07979309